R Notebook

library(readr)
library(magrittr)
library(plotly)
library(dplyr)
library(NbClust)
library(factoextra)
library(tidyr)
library(stringr)
library(ClusterR)
library(dendextend)
library(stringr)
library(tidyr)
library(NbClust)
library(clValid)
library(clusterSim)
library(data.table)

#Task-1

Data1 <- read_csv("Data1.csv")

#K-means clustering
km1 <- kmeans(Data1[,2:4], 7, nstart=30)
kmf <- cbind(Data1[,2:4],Class=km1$cluster)

#Confusion matrix - Kmeans
table(Data1$Class,kmf$Class)

   
     1  2  3  4  5  6  7
  1  0  0  0  0  0  0 32
  2  0  0 30  0  0  0  0
  3  0  0  0  0 30  0  0
  4  0  0  0 30  0  0  0
  5 30  0  0  0  0  0  0
  6  0 30  0  0  0  0  0
  7  0  0  0  0  0 30  0

#Hierarchical clustering
hc1 <- hclust(dist(Data1[,2:4]), method = "single")
dd1 <- as.dendrogram(hc1)
dd1 <- color_branches(dd1, k=7)
#dd1 <- set(dd1, "labels_cex", 0.3)
plot(dd1)

hc1_Class <- cutree(hc1,7)

#Confusion matrix - Hierarchical
table(Data1$Class,hc1_Class)

   hc1_Class
     1  2  3  4  5  6  7
  1 32  0  0  0  0  0  0
  2  0 30  0  0  0  0  0
  3  0  0 30  0  0  0  0
  4  0  0  0 30  0  0  0
  5  0  0  0  0 30  0  0
  6  0  0  0  0  0 30  0
  7  0  0  0  0  0  0 30

#Plotting the original class
plot1<-plot_ly(x=kmf$X1, y=kmf$X2, z=kmf$X3, type="scatter3d", mode="markers", color=as.factor(Data1$Class)) %>%
  layout(title = 'Plot with data points colored based on original class')
plot1

#Plotting the K-means class
plot2<-plot_ly(x=kmf$X1, y=kmf$X2, z=kmf$X3, type="scatter3d", mode="markers", color=as.factor(kmf$Class)) %>%
  layout(title = 'Plot with data points colored based on K-Means output')
plot2

#Plotting the Hierarchical class
plot2<-plot_ly(x=kmf$X1, y=kmf$X2, z=kmf$X3, type="scatter3d", mode="markers", color=as.factor(hc1_Class)) %>%
  layout(title = 'Plot with data points colored based on Hierarchical output')
plot2

#External Validations
kmeans_validation <- external_validation(Data1$Class,kmf$Class,method = "adjusted_rand_index",
                                       summary_stats = TRUE) 

 
---------------------------------------- 
purity                         : 1 
entropy                        : 0 
normalized mutual information  : 1 
variation of information       : 0 
normalized var. of information : 0 
---------------------------------------- 
specificity                    : 1 
sensitivity                    : 1 
precision                      : 1 
recall                         : 1 
F-measure                      : 1 
---------------------------------------- 
accuracy OR rand-index         : 1 
adjusted-rand-index            : 1 
jaccard-index                  : 1 
fowlkes-mallows-index          : 1 
mirkin-metric                  : 0 
---------------------------------------- 

hierarchical_validation <- external_validation(Data1$Class,hc1_Class,method = "adjusted_rand_index",
                                       summary_stats = TRUE)

 
---------------------------------------- 
purity                         : 1 
entropy                        : 0 
normalized mutual information  : 1 
variation of information       : 0 
normalized var. of information : 0 
---------------------------------------- 
specificity                    : 1 
sensitivity                    : 1 
precision                      : 1 
recall                         : 1 
F-measure                      : 1 
---------------------------------------- 
accuracy OR rand-index         : 1 
adjusted-rand-index            : 1 
jaccard-index                  : 1 
fowlkes-mallows-index          : 1 
mirkin-metric                  : 0 
---------------------------------------- 

kmeans_validation

[1] 1

hierarchical_validation

[1] 1

Data2 <- read_csv("Data2.csv")

#K-means clustering
km1 <- kmeans(Data2[,2:4], 4, nstart=30)
kmf <- cbind(Data2[,2:4],Class=km1$cluster)

#Confusion matrix - Kmeans
table(Data2$Class,kmf$Class)

   
      1   2   3   4
  1   0 117  83   0
  2  76  24   0   0
  3   0   0   0 100
  4   4   0   0   0

#Hierarchical clustering(centroid linkage works better)
hc1 <- hclust(dist(Data2[,2:4]), method = "centroid")
dd1 <- as.dendrogram(hc1)
dd1 <- color_branches(dd1, k=4)
#dd1 <- set(dd1, "labels_cex", 0.3)
plot(dd1)

hc1_Class <- cutree(hc1,4)

#Confusion matrix - Hierarchical
table(Data2$Class,hc1_Class)

   hc1_Class
      1   2   3   4
  1 200   0   0   0
  2   0 100   0   0
  3   0   0 100   0
  4   0   0   0   4

#Plotting the original class
plot1<-plot_ly(x=kmf$X, y=kmf$Y, z=kmf$C, type="scatter3d", mode="markers", color=as.factor(Data2$Class)) %>%
  layout(title = 'Plot with data points colored based on original class')
plot1

#Plotting the K-means class
plot2<-plot_ly(x=kmf$X, y=kmf$Y, z=kmf$C, type="scatter3d", mode="markers", color=as.factor(kmf$Class)) %>%
  layout(title = 'Plot with data points colored based on K-Means output')
plot2

#Plotting the Hierarchical class
plot2<-plot_ly(x=kmf$X, y=kmf$Y, z=kmf$C, type="scatter3d", mode="markers", color=as.factor(hc1_Class)) %>%
  layout(title = 'Plot with data points colored based on Hierarchical output')
plot2

#External Validations
kmeans_validation <- external_validation(Data2$Class,kmf$Class,method = "adjusted_rand_index",
                                       summary_stats = TRUE) 

 
---------------------------------------- 
purity                         : 0.9307 
entropy                        : 0.3407 
normalized mutual information  : 0.7255 
variation of information       : 0.9679 
normalized var. of information : 0.4308 
---------------------------------------- 
specificity                    : 0.9397 
sensitivity                    : 0.613 
precision                      : 0.8545 
recall                         : 0.613 
F-measure                      : 0.7139 
---------------------------------------- 
accuracy OR rand-index         : 0.8201 
adjusted-rand-index            : 0.5878 
jaccard-index                  : 0.555 
fowlkes-mallows-index          : 0.7237 
mirkin-metric                  : 29294 
---------------------------------------- 

hierarchical_validation <- external_validation(Data2$Class,hc1_Class,method = "adjusted_rand_index",
                                       summary_stats = TRUE)

 
---------------------------------------- 
purity                         : 1 
entropy                        : 0 
normalized mutual information  : 1 
variation of information       : 0 
normalized var. of information : 0 
---------------------------------------- 
specificity                    : 1 
sensitivity                    : 1 
precision                      : 1 
recall                         : 1 
F-measure                      : 1 
---------------------------------------- 
accuracy OR rand-index         : 1 
adjusted-rand-index            : 1 
jaccard-index                  : 1 
fowlkes-mallows-index          : 1 
mirkin-metric                  : 0 
---------------------------------------- 

kmeans_validation

[1] 0.5877644

hierarchical_validation

[1] 1

#Complete linkage works better for this one

Data3 <- read_csv("Data3.csv")

#K-means clustering
km1 <- kmeans(Data3[,2:4], 4, nstart=30)
kmf <- cbind(Data3[,2:4],Class=km1$cluster)

#Confusion matrix - Kmeans
table(Data3$Class,kmf$Class)

   
      1   2   3   4
  1 100   0   0   0
  2   0   0 100   0
  3   0 100   0   0
  4   0   0   0 100

#Hierarchical clustering(complete linkage works better)
hc1 <- hclust(dist(Data3[,2:4]), method = "complete")
dd1 <- as.dendrogram(hc1)
dd1 <- color_branches(dd1, k=4)
#dd1 <- set(dd1, "labels_cex", 0.3)
plot(dd1)

hc1_Class <- cutree(hc1,4)

#Confusion matrix - Hierarchical
table(Data3$Class,hc1_Class)

   hc1_Class
      1   2   3   4
  1 100   0   0   0
  2   0 100   0   0
  3   0   0  98   2
  4   0   0   0 100

#Plotting the original class
plot1<-plot_ly(x=kmf$X1, y=kmf$X2, z=kmf$X3, type="scatter3d", mode="markers", color=as.factor(Data3$Class)) %>%
  layout(title = 'Plot with data points colored based on original class')
plot1

#Plotting the K-means class
plot2<-plot_ly(x=kmf$X1, y=kmf$X2, z=kmf$X3, type="scatter3d", mode="markers", color=as.factor(kmf$Class)) %>%
  layout(title = 'Plot with data points colored based on K-Means output')
plot2

#Plotting the Hierarchical class
plot2<-plot_ly(x=kmf$X1, y=kmf$X2, z=kmf$X3, type="scatter3d", mode="markers", color=as.factor(hc1_Class)) %>%
  layout(title = 'Plot with data points colored based on Hierarchical output')
plot2

#External Validations
kmeans_validation <- external_validation(Data3$Class,kmf$Class,method = "adjusted_rand_index",
                                       summary_stats = TRUE) 

 
---------------------------------------- 
purity                         : 1 
entropy                        : 0 
normalized mutual information  : 1 
variation of information       : 0 
normalized var. of information : 0 
---------------------------------------- 
specificity                    : 1 
sensitivity                    : 1 
precision                      : 1 
recall                         : 1 
F-measure                      : 1 
---------------------------------------- 
accuracy OR rand-index         : 1 
adjusted-rand-index            : 1 
jaccard-index                  : 1 
fowlkes-mallows-index          : 1 
mirkin-metric                  : 0 
---------------------------------------- 

hierarchical_validation <- external_validation(Data3$Class,hc1_Class,method = "adjusted_rand_index",
                                       summary_stats = TRUE)

 
---------------------------------------- 
purity                         : 0.995 
entropy                        : 0.0177 
normalized mutual information  : 0.9823 
variation of information       : 0.0709 
normalized var. of information : 0.0348 
---------------------------------------- 
specificity                    : 0.9967 
sensitivity                    : 0.9901 
precision                      : 0.9899 
recall                         : 0.9901 
F-measure                      : 0.99 
---------------------------------------- 
accuracy OR rand-index         : 0.995 
adjusted-rand-index            : 0.9867 
jaccard-index                  : 0.9802 
fowlkes-mallows-index          : 0.99 
mirkin-metric                  : 792 
---------------------------------------- 

kmeans_validation

[1] 1

hierarchical_validation

[1] 0.9867009

Data4 <- read_csv("Data4.csv")

#K-means clustering
km1 <- kmeans(Data4[,2:4], 2, nstart=30)
kmf <- cbind(Data4[,2:4],Class=km1$cluster)

#Confusion matrix - Kmeans
table(Data4$Class,kmf$Class)

   
      1   2
  1 327 173
  2 174 326

#Hierarchical clustering
hc1 <- hclust(dist(Data4[,2:4]), method = "single")
dd1 <- as.dendrogram(hc1)
dd1 <- color_branches(dd1, k=2)
#dd1 <- set(dd1, "labels_cex", 0.3)
plot(dd1)

hc1_Class <- cutree(hc1,2)

#Confusion matrix - Hierarchical
table(Data4$Class,hc1_Class)

   hc1_Class
      1   2
  1 500   0
  2   0 500

#Plotting the original class
plot1<-plot_ly(x=kmf$X1, y=kmf$X2, z=kmf$X3, type="scatter3d", mode="markers", color=as.factor(Data4$Class)) %>%
  layout(title = 'Plot with data points colored based on original class')
plot1

#Plotting the K-means class
plot2<-plot_ly(x=kmf$X1, y=kmf$X2, z=kmf$X3, type="scatter3d", mode="markers", color=as.factor(kmf$Class)) %>%
  layout(title = 'Plot with data points colored based on K-Means output')
plot2

#Plotting the Hierarchical class
plot2<-plot_ly(x=kmf$X1, y=kmf$X2, z=kmf$X3, type="scatter3d", mode="markers", color=as.factor(hc1_Class)) %>%
  layout(title = 'Plot with data points colored based on Hierarchical output')
plot2

#External Validations
kmeans_validation <- external_validation(Data4$Class,kmf$Class,method = "adjusted_rand_index",
                                       summary_stats = TRUE) 

 
---------------------------------------- 
purity                         : 0.653 
entropy                        : 0.9314 
normalized mutual information  : 0.0686 
variation of information       : 1.8627 
normalized var. of information : 0.9645 
---------------------------------------- 
specificity                    : 0.5468 
sensitivity                    : 0.5459 
precision                      : 0.5459 
recall                         : 0.5459 
F-measure                      : 0.5459 
---------------------------------------- 
accuracy OR rand-index         : 0.5464 
adjusted-rand-index            : 0.0927 
jaccard-index                  : 0.3754 
fowlkes-mallows-index          : 0.5459 
mirkin-metric                  : 453182 
---------------------------------------- 

hierarchical_validation <- external_validation(Data4$Class,hc1_Class,method = "adjusted_rand_index",
                                       summary_stats = TRUE)

 
---------------------------------------- 
purity                         : 1 
entropy                        : 0 
normalized mutual information  : 1 
variation of information       : 0 
normalized var. of information : 0 
---------------------------------------- 
specificity                    : 1 
sensitivity                    : 1 
precision                      : 1 
recall                         : 1 
F-measure                      : 1 
---------------------------------------- 
accuracy OR rand-index         : 1 
adjusted-rand-index            : 1 
jaccard-index                  : 1 
fowlkes-mallows-index          : 1 
mirkin-metric                  : 0 
---------------------------------------- 

kmeans_validation

[1] 0.09272782

hierarchical_validation

[1] 1

Data5 <- read_csv("Data5.csv")

#K-means clustering
km1 <- kmeans(Data5[,2:4], 2, nstart=30)
kmf <- cbind(Data5[,2:4],Class=km1$cluster)

#Confusion matrix - Kmeans
table(Data5$Class,kmf$Class)

   
      1   2
  1 174 226
  2   0 400

#Hierarchical clustering
hc1 <- hclust(dist(Data5[,2:4]), method = "single")
dd1 <- as.dendrogram(hc1)
dd1 <- color_branches(dd1, k=2)
#dd1 <- set(dd1, "labels_cex", 0.3)
plot(dd1)

hc1_Class <- cutree(hc1,2)

#Confusion matrix - Hierarchical
table(Data5$Class,hc1_Class)

   hc1_Class
      1   2
  1 400   0
  2   0 400

#Plotting the original class
plot1<-plot_ly(x=kmf$X1, y=kmf$X2, z=kmf$X3, type="scatter3d", mode="markers", color=as.factor(Data5$Class)) %>%
  layout(title = 'Plot with data points colored based on original class')
plot1

#Plotting the K-means class
plot2<-plot_ly(x=kmf$X1, y=kmf$X2, z=kmf$X3, type="scatter3d", mode="markers", color=as.factor(kmf$Class)) %>%
  layout(title = 'Plot with data points colored based on K-Means output')
plot2

#Plotting the Hierarchical class
plot2<-plot_ly(x=kmf$X1, y=kmf$X2, z=kmf$X3, type="scatter3d", mode="markers", color=as.factor(hc1_Class)) %>%
  layout(title = 'Plot with data points colored based on Hierarchical output')
plot2

#External Validations
kmeans_validation <- external_validation(Data5$Class,kmf$Class,method = "adjusted_rand_index",
                                       summary_stats = TRUE) 

 
---------------------------------------- 
purity                         : 0.7175 
entropy                        : 0.4939 
normalized mutual information  : 0.2981 
variation of information       : 1.2322 
normalized var. of information : 0.8248 
---------------------------------------- 
specificity                    : 0.435 
sensitivity                    : 0.7536 
precision                      : 0.5709 
recall                         : 0.7536 
F-measure                      : 0.6497 
---------------------------------------- 
accuracy OR rand-index         : 0.5941 
adjusted-rand-index            : 0.1885 
jaccard-index                  : 0.4811 
fowlkes-mallows-index          : 0.6559 
mirkin-metric                  : 259448 
---------------------------------------- 

hierarchical_validation <- external_validation(Data5$Class,hc1_Class,method = "adjusted_rand_index",
                                       summary_stats = TRUE)

 
---------------------------------------- 
purity                         : 1 
entropy                        : 0 
normalized mutual information  : 1 
variation of information       : 0 
normalized var. of information : 0 
---------------------------------------- 
specificity                    : 1 
sensitivity                    : 1 
precision                      : 1 
recall                         : 1 
F-measure                      : 1 
---------------------------------------- 
accuracy OR rand-index         : 1 
adjusted-rand-index            : 1 
jaccard-index                  : 1 
fowlkes-mallows-index          : 1 
mirkin-metric                  : 0 
---------------------------------------- 

kmeans_validation

[1] 0.1885336

hierarchical_validation

[1] 1

Data6 <- read_csv("Data6.csv")
#K-means clustering

km1 <- kmeans(Data6[,2:3], 2, nstart=30)
kmf <- cbind(Data6[,2:3],Class=km1$cluster)

#Confusion matrix - Kmeans
table(Data6$Class,kmf$Class)

   
       1    2
  1   46 2002
  2 1895  153

#Hierarchical clustering(complete linkage works better)
hc1 <- hclust(dist(Data6[,2:3]), method = "complete")
dd1 <- as.dendrogram(hc1)
dd1 <- color_branches(dd1, k=2)
#dd1 <- set(dd1, "labels_cex", 0.3)
plot(dd1)

hc1_Class <- cutree(hc1,2)

#Confusion matrix - Hierarchical
table(Data6$Class,hc1_Class)

   hc1_Class
       1    2
  1 1631  417
  2 2044    4

#Plotting the original class
plot1<-plot_ly(x=kmf$X1, y=kmf$X2, mode="markers", color=as.factor(Data6$Class)) %>%
  layout(title = 'Plot with data points colored based on original class')
plot1

#Plotting the K-means class
plot2<-plot_ly(x=kmf$X1, y=kmf$X2, mode="markers", color=as.factor(kmf$Class)) %>%
  layout(title = 'Plot with data points colored based on K-Means output')
plot2

#Plotting the Hierarchical class
plot2<-plot_ly(x=kmf$X1, y=kmf$X2, mode="markers", color=as.factor(hc1_Class)) %>%
  layout(title = 'Plot with data points colored based on Hierarchical output')
plot2

#External Validations
kmeans_validation <- external_validation(Data6$Class,kmf$Class,method = "adjusted_rand_index",
                                       summary_stats = TRUE) 

 
---------------------------------------- 
purity                         : 0.9514 
entropy                        : 0.2691 
normalized mutual information  : 0.7296 
variation of information       : 0.5403 
normalized var. of information : 0.4257 
---------------------------------------- 
specificity                    : 0.9062 
sensitivity                    : 0.9089 
precision                      : 0.9064 
recall                         : 0.9089 
F-measure                      : 0.9076 
---------------------------------------- 
accuracy OR rand-index         : 0.9075 
adjusted-rand-index            : 0.8151 
jaccard-index                  : 0.8309 
fowlkes-mallows-index          : 0.9076 
mirkin-metric                  : 1551006 
---------------------------------------- 

hierarchical_validation <- external_validation(Data6$Class,hc1_Class,method = "adjusted_rand_index",
                                       summary_stats = TRUE)

 
---------------------------------------- 
purity                         : 0.6008 
entropy                        : 0.3747 
normalized mutual information  : 0.1394 
variation of information       : 1.2717 
normalized var. of information : 0.9251 
---------------------------------------- 
specificity                    : 0.2048 
sensitivity                    : 0.8358 
precision                      : 0.5123 
recall                         : 0.8358 
F-measure                      : 0.6353 
---------------------------------------- 
accuracy OR rand-index         : 0.5202 
adjusted-rand-index            : 0.0406 
jaccard-index                  : 0.4655 
fowlkes-mallows-index          : 0.6544 
mirkin-metric                  : 8047470 
---------------------------------------- 

kmeans_validation

[1] 0.8150606

hierarchical_validation

[1] 0.04058039

Data7 <- read_csv("Data7.csv")

#K-means clustering
km1 <- kmeans(Data7[,2:3], 6, nstart=30)
kmf <- cbind(Data7[,2:3],Class=km1$cluster)

#Confusion matrix - Kmeans
table(Data7$Class,kmf$Class)

   
      1   2   3   4   5   6
  1 395   0   0   0   0   0
  2   0  71  76  55  86  75
  3   0   0   0   0   0   3
  4   0   0   0   0   3   0
  5   0   0   3   0   0   0
  6   0   0   0   3   0   0

#Hierarchical clustering
hc1 <- hclust(dist(Data7[,2:3]), method = "single")
dd1 <- as.dendrogram(hc1)
dd1 <- color_branches(dd1, k=6)
#dd1 <- set(dd1, "labels_cex", 0.3)
plot(dd1)

hc1_Class <- cutree(hc1,6)

#Confusion matrix - Hierarchical
table(Data7$Class,hc1_Class)

   hc1_Class
      1   2   3   4   5   6
  1   0   0   0   0 395   0
  2   0   0   0   0   0 363
  3   0   0   0   3   0   0
  4   0   3   0   0   0   0
  5   3   0   0   0   0   0
  6   0   0   3   0   0   0

#Plotting the original class
plot1<-plot_ly(x=kmf$X1, y=kmf$X2, color=as.factor(Data7$Class)) %>%
  layout(title = 'Plot with data points colored based on original class')
plot1

#Plotting the K-means class
plot2<-plot_ly(x=kmf$X1, y=kmf$X2, color=as.factor(kmf$Class)) %>%
  layout(title = 'Plot with data points colored based on K-Means output')
plot2

#Plotting the Hierarchical class
plot2<-plot_ly(x=kmf$X1, y=kmf$X2, mode="markers", color=as.factor(hc1_Class)) %>%
  layout(title = 'Plot with data points colored based on Hierarchical output')
plot2

#External Validations
kmeans_validation <- external_validation(Data7$Class,kmf$Class,method = "adjusted_rand_index",
                                       summary_stats = TRUE) 

 
---------------------------------------- 
purity                         : 0.9844 
entropy                        : 0.4208 
normalized mutual information  : 0.6367 
variation of information       : 1.1822 
normalized var. of information : 0.533 
---------------------------------------- 
specificity                    : 0.9943 
sensitivity                    : 0.6346 
precision                      : 0.9905 
recall                         : 0.6346 
F-measure                      : 0.7735 
---------------------------------------- 
accuracy OR rand-index         : 0.8199 
adjusted-rand-index            : 0.6355 
jaccard-index                  : 0.6307 
fowlkes-mallows-index          : 0.7928 
mirkin-metric                  : 106658 
---------------------------------------- 

hierarchical_validation <- external_validation(Data7$Class,hc1_Class,method = "adjusted_rand_index",
                                       summary_stats = TRUE)

 
---------------------------------------- 
purity                         : 1 
entropy                        : 0 
normalized mutual information  : 1 
variation of information       : 0 
normalized var. of information : 0 
---------------------------------------- 
specificity                    : 1 
sensitivity                    : 1 
precision                      : 1 
recall                         : 1 
F-measure                      : 1 
---------------------------------------- 
accuracy OR rand-index         : 1 
adjusted-rand-index            : 1 
jaccard-index                  : 1 
fowlkes-mallows-index          : 1 
mirkin-metric                  : 0 
---------------------------------------- 

kmeans_validation

[1] 0.6355487

hierarchical_validation

[1] 1

Data8 <- read_csv("Data8.csv")
#K-means clustering

km1 <- kmeans(Data8[,2:4], 1, nstart=30)
kmf <- cbind(Data8[,2:4],Class=km1$cluster)

#Confusion matrix - Kmeans
table(Data8$Class,kmf$Class)

   
       1
  1 4002

#Hierarchical clustering
hc1 <- hclust(dist(Data8[,2:4]), method = "single")
dd1 <- as.dendrogram(hc1)
dd1 <- color_branches(dd1, k=1)
#dd1 <- set(dd1, "labels_cex", 0.3)
plot(dd1)

hc1_Class <- cutree(hc1,1)

#Confusion matrix - Hierarchical
table(Data8$Class,hc1_Class)

   hc1_Class
       1
  1 4002

#Plotting the original class
plot1<-plot_ly(x=kmf$X1, y=kmf$X2, z=kmf$X3, type="scatter3d", mode="markers", color=as.factor(Data8$Class)) %>%
  layout(title = 'Plot with data points colored based on original class')
plot1

#Plotting the K-means class
plot2<-plot_ly(x=kmf$X1, y=kmf$X2, z=kmf$X3, type="scatter3d", mode="markers", color=as.factor(kmf$Class)) %>%
  layout(title = 'Plot with data points colored based on K-Means output')
plot2

#Plotting the Hierarchical class
plot2<-plot_ly(x=kmf$X1, y=kmf$X2, z=kmf$X3, type="scatter3d", mode="markers", color=as.factor(hc1_Class)) %>%
  layout(title = 'Plot with data points colored based on Hierarchical output')
plot2

#External Validations
kmeans_validation <- external_validation(Data8$Class,kmf$Class,method = "adjusted_rand_index",
                                       summary_stats = TRUE) 

 
---------------------------------------- 
purity                         : 1 
entropy                        : NaN 
normalized mutual information  : 1 
variation of information       : 0 
normalized var. of information : 1 
---------------------------------------- 
specificity                    : NaN 
sensitivity                    : 1 
precision                      : 1 
recall                         : 1 
F-measure                      : 1 
---------------------------------------- 
accuracy OR rand-index         : 1 
adjusted-rand-index            : NaN 
jaccard-index                  : 1 
fowlkes-mallows-index          : 1 
mirkin-metric                  : 0 
---------------------------------------- 

hierarchical_validation <- external_validation(Data8$Class,hc1_Class,method = "adjusted_rand_index",
                                       summary_stats = TRUE)

 
---------------------------------------- 
purity                         : 1 
entropy                        : NaN 
normalized mutual information  : 1 
variation of information       : 0 
normalized var. of information : 1 
---------------------------------------- 
specificity                    : NaN 
sensitivity                    : 1 
precision                      : 1 
recall                         : 1 
F-measure                      : 1 
---------------------------------------- 
accuracy OR rand-index         : 1 
adjusted-rand-index            : NaN 
jaccard-index                  : 1 
fowlkes-mallows-index          : 1 
mirkin-metric                  : 0 
---------------------------------------- 

kmeans_validation

[1] NaN

hierarchical_validation

[1] NaN

#Task-2

world_i1 <- read_csv("World Indicators.csv")

world_i1$`Business Tax Rate` <- gsub("%","",world_i1$`Business Tax Rate`)
world_i1$`Health Exp/Capita` <- substr(world_i1$`Health Exp/Capita`,2,length(world_i1$`Health Exp/Capita`))
world_i1$GDP <- substr(world_i1$GDP,2,length(world_i1$GDP))

world_i1$GDP <- gsub(",","",world_i1$GDP)
world_i1$`Health Exp/Capita` <- gsub(",","",world_i1$`Health Exp/Capita`)

world_i1$`Business Tax Rate` <- as.numeric(world_i1$`Business Tax Rate`)
world_i1$`Health Exp/Capita` <- as.numeric(world_i1$`Health Exp/Capita`)
world_i1$GDP <- as.numeric(world_i1$GDP)

#Removing the two columns with maximum number of null values and scaling

World_i2 <- world_i1[,-c(4,11)] %>%
  drop_na()
df <- data.frame(scale(World_i2[,1:16]))

#Finding the optimal number of clusters

#Elbow method
fviz_nbclust(df[,1:16] , kmeans , method = 'wss')

#Silhoutte method
fviz_nbclust(df[,1:16] , kmeans , method = 'silhouette')

#Finding distance
Dist_KM <- get_dist(df)

#Visualizing the distance values
fviz_dist(Dist_KM)

#As both the methods show around 2 as the optimal number, we cluster them into two classes below
km <- kmeans(df[,1:16] , 2 , nstart = 20)

#Visualizing the cluster from k-means
fviz_cluster(km , data = df[,1:16])

km$cluster

  [1] 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 1 1 2 2 1 2
 [57] 1 1 2 2 1 1 1 2 2 1 1 2 2 2 1 1 2 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[113] 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 2 2 1 2 2 2 2 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 2 1 1 1 1 1 2 1
[169] 1 1 1

df$KM <- km$cluster
World_i2$KM <- km$cluster
#Internal validation for k-means - validated using dunn index
dunn_km <- dunn(clusters = df$KM , Data = df[,1:16])

dunn_km

[1] 0.06697056

km$centers

  Birth.Rate Business.Tax.Rate Days.to.Start.Business        GDP Health.Exp...GDP Health.Exp.Capita Hours.to.do.Tax
1 -0.7087267        -0.1429606             -0.1949461  0.1732969        0.1399650         0.3796016     -0.04960754
2  0.9514413         0.1919197              0.2617084 -0.2326451       -0.1878983        -0.5096021      0.06659642
  Infant.Mortality.Rate Internet.Usage Life.Expectancy.Female Life.Expectancy.Male Mobile.Phone.Usage
1            -0.6904214      0.6867375              0.6891531            0.6674966           0.600936
2             0.9268671     -0.9219216             -0.9251645           -0.8960913          -0.806736
  Population.0.14 Population.15.64 Population.65. Population.Urban
1      -0.7377098        0.6860028      0.5746374        0.5496109
2       0.9903501       -0.9209353     -0.7714310       -0.7378338

#Three classes
km <- kmeans(df[,1:16] , 3 , nstart = 20)

#Visualizing the cluster from k-means
fviz_cluster(km , data = df[,1:16])

km$cluster

  [1] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 2 1 2 1 1 1 1 2 1 1 1 2 2 1 2 2 1
 [57] 2 2 1 2 3 2 3 2 1 2 2 1 1 2 2 2 1 2 1 2 2 2 3 2 3 2 2 2 2 2 3 2 3 3 3 3 2 3 3 3 2 2 3 2 3 2 2 3 3 2 3 2 2 2 2 3
[113] 3 3 3 2 2 3 2 2 1 2 2 2 2 2 2 2 2 1 3 2 1 1 3 1 1 1 1 2 2 2 2 2 1 2 3 2 2 2 2 2 2 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2
[169] 3 2 2

#Internal validation for k-means - validated using dunn index
dunn_km <- dunn(clusters = df$KM , Data = df[,1:16])

dunn_km

[1] 0.06697056

km$centers

  Birth.Rate Business.Tax.Rate Days.to.Start.Business         GDP Health.Exp...GDP Health.Exp.Capita Hours.to.do.Tax
1  1.0977304         0.2220355            0.125770071 -0.24189747       -0.1675895        -0.5174629      0.12191236
2 -0.5187961        -0.1321157            0.007281763 -0.08747886       -0.2478830        -0.2458843      0.05915505
3 -1.0236822        -0.1213366           -0.327716114  0.86203103        1.1878672         2.0293338     -0.48196895
  Infant.Mortality.Rate Internet.Usage Life.Expectancy.Female Life.Expectancy.Male Mobile.Phone.Usage
1             1.0827672     -0.9881109             -1.0659632           -1.0183934         -0.9344346
2            -0.5315755      0.2826238              0.4572462            0.3817182          0.5353050
3            -0.9471209      1.5029167              1.1408266            1.2637652          0.5759372
  Population.0.14 Population.15.64 Population.65. Population.Urban
1       1.1086122       -1.0757826     -0.8045752       -0.8069778
2      -0.4960104        0.6698899      0.1124584        0.2877398
3      -1.1219121        0.4939742      1.5948711        1.0478823

#Dunn index yields a larger value when k=2 for k-means

#Hierarchical clustering with "single" linkage
labs <- World_i2$Country[1:171]
hc.single <- hclust(dist(df[,1:16]) , method = "single")
dd <- as.dendrogram(hc.single)
dd <- color_branches(dd, k=2)
plot(dd)

plot(hc.single, labels = labs)

#Hierarchical clustering with "average" linkage
hc.average <- hclust(dist(df[,1:16]) , method = "average")
dd <- as.dendrogram(hc.average)
dd <- color_branches(dd, k=2)
plot(dd)

plot(hc.average, labels = labs)

#Hierarchical clustering with "complete" linkage
hc.complete <- hclust(dist(df[,1:16]) , method = "complete")
dd <- as.dendrogram(hc.complete)
dd <- color_branches(dd, k=2)
plot(dd)

plot(hc.complete, labels = labs)

#Internal validation for Hierarchical clustering
#Two clusters
Dist <- dist(df[,1:16] , method = 'euclidean')
nc_1 <- 2
hc_cluster1 <- cutree(hc.complete,nc_1)
dunn(Dist, hc_cluster1)

[1] 0.5198649

df$hc_cluster <- hc_cluster1
World_i2$hc_cluster <- hc_cluster1
#Three clusters
Dist <- dist(df[,1:16] , method = 'euclidean')
nc_1 <- 3
hc_cluster1 <- cutree(hc.complete,nc_1)

dunn(Dist, hc_cluster1)

[1] 0.564507

#Dunn index yields a larger value when k=3 for hierarchical clustering

#Overall, the best result is obtained with hierarchical clustering with k=3 (validated using dunn index). Hence using the same to categorize the countries

df_cluster_1 <- subset(World_i2 , hc_cluster1 == 1)
df_cluster_2 <- subset(World_i2 , hc_cluster1 == 2)
df_cluster_3 <- subset(World_i2 , hc_cluster1 == 3)

#Countries in each group
c1 <- df_cluster_1$Country
c2 <- df_cluster_2$Country
c3 <- df_cluster_3$Country
internal_validation <- clValid(df[,1:16],2:7,clMethods=c("hierarchical","kmeans"),validation="internal")
summary(internal_validation)

Clustering Methods:
 hierarchical kmeans 

Cluster sizes:
 2 3 4 5 6 7 

Validation Measures:
                                 2       3       4       5       6       7
                                                                          
hierarchical Connectivity   2.9290  5.8579  8.7869 13.3238 31.6563 34.5853
             Dunn           0.5199  0.5645  0.5167  0.3359  0.1953  0.1953
             Silhouette     0.5979  0.5731  0.5168  0.4223  0.3572  0.3160
kmeans       Connectivity  29.0286 30.6075 43.5087 46.6631 40.0024 52.5012
             Dunn           0.0670  0.0705  0.0687  0.0713  0.1267  0.1100
             Silhouette     0.3611  0.3639  0.2991  0.2891  0.3716  0.3049

Optimal Scores:

plot(internal_validation)

#Plotting

#We have decided to find the correlation between each column and use the columns that have large correlation value for ploting and colored them based on clasees

#correlation function
cor(World_i2[,1:16])

                       Birth Rate Business Tax Rate Days to Start Business         GDP Health Exp % GDP
Birth Rate              1.0000000        0.25832327             0.10627023 -0.23384759     -0.221273544
Business Tax Rate       0.2583233        1.00000000             0.02645857  0.02543613     -0.078449904
Days to Start Business  0.1062702        0.02645857             1.00000000 -0.04970137     -0.148395627
GDP                    -0.2338476        0.02543613            -0.04970137  1.00000000      0.338555911
Health Exp % GDP       -0.2212735       -0.07844990            -0.14839563  0.33855591      1.000000000
Health Exp/Capita      -0.4885708       -0.09342338            -0.13000616  0.43195417      0.494636086
Hours to do Tax         0.1139401        0.15201992             0.14719366  0.04531425     -0.082171525
Infant Mortality Rate   0.8728444        0.25331039             0.11504030 -0.19652001     -0.142575915
Internet Usage         -0.8096124       -0.19386059            -0.17351210  0.25588950      0.281448992
Life Expectancy Female -0.8683710       -0.20693869            -0.12855991  0.21897245      0.169783887
Life Expectancy Male   -0.8375751       -0.23108486            -0.14802986  0.23636298      0.190877771
Mobile Phone Usage     -0.6706084       -0.22394032            -0.08859167  0.04812196     -0.014945233
Population 0-14         0.9642443        0.20842064             0.14390213 -0.24386520     -0.225838389
Population 15-64       -0.8777268       -0.24823919            -0.09475062  0.15272895      0.001004394
Population 65+         -0.7758136       -0.09118757            -0.16290533  0.28595966      0.449373106
Population Urban       -0.5889220       -0.09274097            -0.05135881  0.22205852      0.162976604
                       Health Exp/Capita Hours to do Tax Infant Mortality Rate Internet Usage Life Expectancy Female
Birth Rate                   -0.48857076      0.11394011             0.8728444     -0.8096124             -0.8683710
Business Tax Rate            -0.09342338      0.15201992             0.2533104     -0.1938606             -0.2069387
Days to Start Business       -0.13000616      0.14719366             0.1150403     -0.1735121             -0.1285599
GDP                           0.43195417      0.04531425            -0.1965200      0.2558895              0.2189724
Health Exp % GDP              0.49463609     -0.08217153            -0.1425759      0.2814490              0.1697839
Health Exp/Capita             1.00000000     -0.21585274            -0.4646887      0.7232246              0.5250518
Hours to do Tax              -0.21585274      1.00000000             0.1677532     -0.1782408             -0.1365328
Infant Mortality Rate        -0.46468871      0.16775316             1.0000000     -0.7827817             -0.9261500
Internet Usage                0.72322459     -0.17824084            -0.7827817      1.0000000              0.7994866
Life Expectancy Female        0.52505178     -0.13653281            -0.9261500      0.7994866              1.0000000
Life Expectancy Male          0.57618819     -0.18072133            -0.9021864      0.8120771              0.9751152
Mobile Phone Usage            0.33115351     -0.03731317            -0.6903296      0.6486685              0.6410972
Population 0-14              -0.52558017      0.12541678             0.8393445     -0.8446817             -0.8381414
Population 15-64              0.30542898     -0.13468736            -0.7715820      0.7128263              0.7428294
Population 65+                0.64962746     -0.07431018            -0.6654919      0.7531107              0.7009784
Population Urban              0.52094854      0.00397962            -0.5837639      0.6884567              0.6147325
                       Life Expectancy Male Mobile Phone Usage Population 0-14 Population 15-64 Population 65+
Birth Rate                       -0.8375751        -0.67060841       0.9642443     -0.877726752    -0.77581357
Business Tax Rate                -0.2310849        -0.22394032       0.2084206     -0.248239186    -0.09118757
Days to Start Business           -0.1480299        -0.08859167       0.1439021     -0.094750616    -0.16290533
GDP                               0.2363630         0.04812196      -0.2438652      0.152728948     0.28595966
Health Exp % GDP                  0.1908778        -0.01494523      -0.2258384      0.001004394     0.44937311
Health Exp/Capita                 0.5761882         0.33115351      -0.5255802      0.305428983     0.64962746
Hours to do Tax                  -0.1807213        -0.03731317       0.1254168     -0.134687360    -0.07431018
Infant Mortality Rate            -0.9021864        -0.69032956       0.8393445     -0.771582041    -0.66549191
Internet Usage                    0.8120771         0.64866852      -0.8446817      0.712826274     0.75311072
Life Expectancy Female            0.9751152         0.64109715      -0.8381414      0.742829375     0.70097835
Life Expectancy Male              1.0000000         0.60645028      -0.8031596      0.721028735     0.65980935
Mobile Phone Usage                0.6064503         1.00000000      -0.6832376      0.655548188     0.50566329
Population 0-14                  -0.8031596        -0.68323759       1.0000000     -0.899067027    -0.81912396
Population 15-64                  0.7210287         0.65554819      -0.8990670      1.000000000     0.48534210
Population 65+                    0.6598094         0.50566329      -0.8191240      0.485342103     1.00000000
Population Urban                  0.6292576         0.57532418      -0.6211391      0.564644276     0.50060369
                       Population Urban
Birth Rate                  -0.58892197
Business Tax Rate           -0.09274097
Days to Start Business      -0.05135881
GDP                          0.22205852
Health Exp % GDP             0.16297660
Health Exp/Capita            0.52094854
Hours to do Tax              0.00397962
Infant Mortality Rate       -0.58376391
Internet Usage               0.68845669
Life Expectancy Female       0.61473249
Life Expectancy Male         0.62925757
Mobile Phone Usage           0.57532418
Population 0-14             -0.62113912
Population 15-64             0.56464428
Population 65+               0.50060369
Population Urban             1.00000000

#Plot1 #Population 0-14 and birthrate seems to have large correlation

plot1<-plot_ly(x=World_i2$`Birth Rate`, y=World_i2$`Population 0-14`, mode="markers", color=as.factor(World_i2$hc_cluster)) %>%
  layout(title = 'Birthrate vs Population 0-14')
plot1

#Plot2 #Life expectancy female and birthrate seems to have a correlation

plot2<-plot_ly(x=World_i2$`Birth Rate`, y=World_i2$`Life Expectancy Female`, mode="markers", color=as.factor(World_i2$hc_cluster)) %>%
  layout(title = 'Birthrate vs Life expectancy female')
plot2

#Plot3 #Health Exp/Capita and internet usage also looks like there is a correlation

plot3<-plot_ly(x=World_i2$`Health Exp/Capita`, y=World_i2$`Internet Usage`, mode="markers", color=as.factor(World_i2$hc_cluster)) %>%
  layout(title = 'Health Exp/Capita vs Internet usage')
plot3